integral from 1 to 12 of 4e^{0.1t}

Lösung

\int_{1}^{12} 4 e^{0.1 t} d t

88.59784 \dots

Schritte zur Lösung

\int_{1}^{12} 4 e^{0.1 t} d t

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int_{1}^{12} e^{0.1 t} d t

Wende U-Substitution an

= 4 \cdot \int_{0.1}^{1.2} e^{u} \frac{1}{0.1} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \frac{1}{0.1} \cdot \int_{0.1}^{1.2} e^{u} d u

Vereinfache

= 4 \cdot 10 \cdot \int_{0.1}^{1.2} e^{u} d u

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= 4 \cdot 10 [e^{u}]_{0.1}^{1.2}

Vereinfache

= 40 [e^{u}]_{0.1}^{1.2}

Berechne die Grenzen:

2.21494 \dots

= 40 \cdot 2.21494 \dots

Vereinfache

= 88.59784 \dots

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